In my experience the LPIC and Red Hat certifications are more recognized, Linux Foundation is trying to gain some respect but it might take some more time. The problem is, LPIC-1 is just an entry level, which means you’d need to do LPIC-2 as well, thus 4 tests and it’s rather expensive as well!
I think doing both LF at you home will bring you results faster.
But of course this decision is up to you!
Good luck and success!